User:Ulf Rehmann/sandbox statprob/

\begin{table} '''Table 1.''' A class of stationary correlation models for longitudinal count data and basic properties. <center> \begin{array}{ccc} Model & Dynamic relationship & Mean-variance \\ && \& Correlations \\ \hline AR(1) & y_{it}=\rho * y_{i,t-1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ & y_{i1}\sim Poi(\mu_{i\cdot}) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ & d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ && =\rho^{\ell} \\ \hline MA(1) & y_{it}=\rho * d_{i,t-1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ & y_{i1}=d_{i1} \sim Poi(\mu_{i\cdot}/(1+\rho)) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ & d_{it} \sim P(\mu_{i\cdot}/(1+\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ && '"`UNIQ-MathJax2-QINU`"' \\ \hline EQC & y_{it}=\rho * y_{i1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ & y_{i1}\sim Poi(\mu_{i\cdot}) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ & d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ && =\rho \\ \hline \end{array}

\end{table}